Measurement of intensity of turbulence in water by dye diffusion

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or ed tO

NAVY DEPARTMENT
THE DAVID W. TAYLOR MODEL BASIN
Washington 7, D.C.

\W H OTN
DOCUMENT |
COLLECTION

MEASUREMENT OF INTENSITY OF TURBULENCE
IN WATER BY DYE DIFFUSION
NS 713=049

by
M. S. Macovsky, W. L. Stracke, and J. V. Wehausen

July 1949 Report 700

7 OEb2EOO TOEO O

MTA

1OHM/18lWN

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MEASUREMENT OF INTENSITY OF TURBULENCE
IN WATER BY DYE DIFFUSION

by
M. S. Macovsky, W. L. Stracke, and J. V. Wehausen

ABSTRACT

This report describes exploratory experiments which were
made to develop a means for measuring intensity of turbulence
in water by a method of dye diffusion analogous to the method
developed by Schubauer using heat diffusion in air. Although
the method was dropped before the experimental technique was
refined, the work completed indicates that the method can be
used under certain circumstances to give fairly reliable re-
sults. Some of the restrictions on the method, some necessary,
improvements in the technique, and some methods of data correce
tion are discussed. 3

INTRODUCTION

This report describes some exploratory experiments which
‘were made in order to develop a method for measuring turbulence
intensity in water by a method of dye diffusion analogous to
the heat diffusion method used by Schubauer (1)*. Although
the experiments were carried out somewhat crudely, they have
perhaps served their purpose in that they indicate that the
method can be used successfully and they point out the places
where greater care needs to be taken. The two values of in-
tensity obtained as a result of the experiments are in fairly
good agreement with results obtained under the same circumstances
with a hot-wire velocity meter for water. The method was not
pursued further since a hot+wire velocity meter had been develop-
ed which was satisfactory for water and which was much more
versatile in use.

It has been known for some time that the rate of diffusion
of a substance from a source in a turbulent stream can be used
to measure the intensity of the transverse component of the tur-
bulent fluctuations and also at least one of the several scales
of turbulence which may be defined. The theoretical justifica-
tions for the method was given by G. I. Taylor (2)(3) and the
method was used by Schubauer (1) to measure turbulence in a
wind tunnel from the measured temperature distribution behind
a heated wire. Diffusion methods have also been used in water
by Kalinske, Robertson, and Van Driest (4),(5),(6).in order to
determine the intensity of turbulence. In these experiments the
diffusing substance was small particles and their meanderings

* Numbers in parentheses indicate references on page 13,

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had to be recorded photographically and then analyzed statistic-
cally, The present method has the advantage that the statistical
analysis is bypassed since average quantities are measured directly.
On the other hand, it has some disadvantage in that the operation
of measurement alters the quantities being measured and makes
substantial correction necessary.

OQUTLINE OF THE METHOD

The idea of the method will be briefly described before pro-
ceding to a more detailed description of experimental procedures
A schematic diagram of the equipment is given in Figure lo Ina
turbulent stream of water a small element of dye emitted from the
injector will tend to meander from the axis of the injector in an
erratic fashion following the erratic motion of the water. Ele-
ments leaving the injector at different times, not too close to-
gether, will generally follow quite different paths. If the
sampler is now fixed in some definite position and a sample of
the water passing by withdrawn through it at a uniform rate over
a sufficiently long time interval, the resulting sample will be
more or less strongly colored depending upon how frequently ele-
ments of dye are carried as far off the axis as the sampler is
situated, One expects the greatest density of dye if the sampler
is right on the axis and steadily decreasing amounts as it is
moved off the axis, If the sample is taken over too short a time
interval, the sample may give a concentration of dye deviating
too much from the true average; it is conceivable that such a
sample might be almost pure water or almost pure dye, depending
upon the short time interval in which the sample was taken. The
actual concentration of dye was measured by means of an electro-
photometer which had been calibrated for the dye being used.
However, it is not difficult to think of other schemes for doing
the same thing.

If the turbulence of the water is very intense, one will
expect the dye elements to wander farther from the axis, on
the average, in a given distance downstream, than if the turbu-
lence is not very intense. Consequently, the rate of spreading
of the average dye wake gives a measure of the intensity of
turbulence near the end of the injector. The discussion of the
method for obtaining a quantitative measure of the turbulence
is described in the section dealing with the analysis of the
data.

In the case of heat diffusion behind a heated wire it is
necessary to make a correction for the molecular diffusion of
heat. which is taking place as well as the turbulent diffusion.
In the case of dye diffusion the molecular diffusion can be
completely neglected, for the amount is very small during the
time intervals involved.

TDi ie

DESCRIPTION OF PROCEDURE

The experiments were carried out in the 1/22=-scale model
of the circulating water channel of the Taylor Model Basin,
(Figure 2), The test section is 12 inches across and the water
was about 6 inches deep during the experiments. The velocity
used was about 1.6 ft./sec.

At the entrance to the test section a brass grid was placed
as a source of turbulence. The mesh width was 0.75 in. and the
wire diameter 0.15 in. A length of brass tubing, inside diameter
0.035 in., outside diameter 0.060 in., was then placed in the
-test section in the manner shown schematically in Figure 1. The
downstream end of the horizontal section of the tuhing was located
15 and 22 mesh lengths from the grid. The other end of the tubing
eventually led to a jar containing the dye to be used. In order
to be able to control the rate of flow of dye through the tubing
the jar was connected with a flask of compressed air equipped
with a valve. Measurement of the discharge rate showed that the
average velocity through the release tube was about 2.2 ft/sec.

To measure the average concentration of dye at positions
downstream from the end of the dye release tube, a 3-in. length
of the same brass tubing was attached to the movable sampler
shown in Figure 3. This probe was rigidly clamped to the channel
carriage in a position such that the sampler lay in the same
vertical plane as the release tube. By means of the probe
micrometer screw, this sampler could be traversed vertically in
any desired increment with an accuracy of O.O0Ql-in. to a total
displacement of 3 in. In order to extract a sample of water
from some position downstream of the release tube a 25 cc pipette
was connected to the sampling tube by means of a short length of
rubber tubing and a sample sucked out. Tests with a stop watch
showed that the average velocity of the water passing through the
end of the sampling tube was about 5 ft/sec.

The dye solution used in these experiments was made by
dissolving about 1 gm of Ponceau red, a water-soluble food dye,
in 4 liters of water. The concentration of a sample was measured
by means of a Fisher Electrophotometer. Such measurements are
generally considered to be accurate to about 1 percent. No series
of experiments to determine the accuracy of this instrument was
made since the exploratory nature of the setup did not seem to
warrent them. In order to determine whether the length of time
over which a given sample was taken was sufficient to give a con=
centration close to the average concentration at that point,
several of these samples were taken twice. The maximum changes
were of the order of 8 percent. In order to take account of the
gradual coloring of all the water in the channel, a sample of
the channel water was also taken after every set of five measure-
ments. The correction for the darkening of the channel water was
surprizingly little considering how noticeable the coloring was
to the eye. 3

Mer RAL) a
Tah ban

Surveys of the distribution of average dye concentration
across-stream in the vertical plane were made at distances down-
stream of 1/2, 3/4, 1, and 1 1/2 in.

ANALYSIS OF RESULTS

In Figures 4 and 5 are plotted the points obtained from
these surveys at the various stations downstream from the injector.
Note that the y-coordinate in these figures is measured from a
displaced origin, not from the axis of symmetry. A smooth curve
has been faired through each set of data. The ordinates give the
ratio of the concentration of the measured sample to the concentra=
tion of the original solution. These curves will be called con-
centration curves. Actually, they are traces in a vertical plane
of a concentration surface. Although it was not verified, it
will be assumed that these surfaces are axially symmetric so that
the surface could be generated by revolving the measured curve
about its symmetry axis.

Measurements of other experimenters indicate that one can
expect the concentration surface to be an axially symmetric
Gaussian error surface. One would then expect the concentration
curves to fit an equation of the form

pedal /al Mee

FC) ana* =
where r is the distance from the axis and A and o are constants
depending upon the station under consideration, The constant A
gives a measure of the total amount of dye passing a given stations
o is a measure of the width of the dye wake, the distance from
the axis to the inflection of the concentration surface, Actually,
however, the effect of the finite size of opening of the sampler
will be to deform this curve, the deformation being greater, the
greater the size of opening of the sampler relative to the
quantity o@. Indeed, . in case the rate of flow of water entering
the sampler is greater than the free-stream velocity the effective
size of the opening is further increased. In the present experi-=
ments the average velocity of water in the sampler was about three
times the free-stream velocity. This corresponds to an effective
diameter of the sampler about 1.7 times its actual diameter.
Since the actual sampler diameter was 0.035 in., we shall take
as effective sampler diameter 0.060 in. The effective radius
of the sampler will hereafter be denoted by R.

The chief difficulty in analyzing the data is in determining
from the measured, deformed curves the constants A and o of the
true curves, The” theory for the method of correction is developed
in the appendix and is based upon the assumption that the true
concentration surface is a circuler Gaussian surface. The pro-
cedure for finding o was as follows. First, the experimental
curves were treated as if they were Gaussian curves. In this

@- 4 «=

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beh
ppl

x

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i

ah

i

ae

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i ros
nha] cm
ae
a oi

oa

sl ”

hs

case the area under the curve between the values r2z@andre-o
divided by the total area under the curve is 0.68. If g(r) de-
notes the curve faired through the measured points, this entailed
measuring the areas fe g(s)ds for enough values of r to plot a

curve, which will be denoted by 2G(r). A value GO was then
determined from G(gg) = 0.68G(). This will not, of course, be
the true value of go. The true value, denoted by ©], was then
determined by the method described in the appendix. Two methods
for determining A are described in the appendix. Tests with two
different curves gave nearly the same value for A for each method
so that it was decided to use the second method which involved
somewhat less labor. The results of this analysis are shown in
the following table. The meanings of the letters X, L, and M are
shown in Figure 1.

1.00 0.027 0,022 1.30x1073! 0.75 1.21x1073
1.25. 0.040 6.037 1.42x10-3} 1.00 : 1.46x10-3
1.5! J oi O36 _1.:

* The values of @) and A are omitted for the station L/M = 15,
X = 0.75 in. beGause a corrected value of @%) did not seem to
exist. This would seem to indicate that the measured value of
@> = 0.017 in. was impossible, at least under the assumption that
the effective value of the sampler diameter was 0.060 in. Dis-
crepancies of this sort could probably be avoided in a more care-
fully controlled experiment in which the rate of removal of
fluid through the sampler was adjusted to be equal to or less
than the free-stream velocity.

Since the total amount of dye passing in unit time each
station downstream of the injector should be the same, one will
expect A to be a constant. The constancy of A provides a sort
of check upon the accuracy of the experiments, providing, of
course, that the rate of dye release has been kept constant dur-
ing all the measurements. Inspection of the values of A in the
table above shows that the variation is not large with the ex-
ception of two points; the value of A for L/M = 15 and X s 1.50
in. is too large by almost a factor of 2, whereas the value for
L/M = 22 and X = 0.50 in. is too small by a substantial amount.
This discrepancy may have arisen from the general crudeness of
the experiments or perhaps was caused by an actual error.

The transverse intensity of turbulence may now be com-
puted from the values of @. Let X be the distance measured
downstream from the end of the dye injector and let Y be
distance measured vertically. if a particle starts at the

Sabie

end of the injector tube and moves downstream in a turbulent flow
its trajectory might appear as follows:
y;

= ane aes Pi iit oa x

Let the vertical velocity component of the particle at time t-.
after leaving the injector be v(t). Then the transverse, displace-_
ment y(t) of the particle at time t is given by y(t) = f v(v)dt.
The mean square displacement is then given by ete
te boone. aie ae
yw) = ff vinviaidr de

° so

or, introducing the correlation coefficient

Fn ay cr) = Vitivia) / Vityv'"(s) : pleeyy ae :

——

t .t
yt) = j, Hf vi(r) vile) R (7,0) dtdo

it should be noted that the means are not time averages of the
functions v2(t) and y2(t), but are ensemble averages taken over
a large number of particles. From the last equation one easily
derives

ees t E 5
2 Z = re ee ’ ? unc OSeseliie , 5
d, y(t) = 2 v4 2dvinf vo) Rit,ado avin {vin 2 Rito) da
and, setting t = 0,
,—— 2
do y*(o.) = 2 vo)
d t*

One may recast this formula as follows:

Ss ey Halted ona
a y*(o) = |2/y*0 dy yro) |= ad Vy%o +21 Fad, /y7 =? y'7o)

dt?
d /yto) = Vo)
ade’?

or, finally,

If one now makes the assumption that the fluctuations of velocity
in the longitudinal direction are small compared with the free-
stream velocity U, one may write, approximately, X = Ut and write
the last equation above

fy yo) = Vl) /U
x
a6

ae a
nee

The standard deviati o (xX), of the concentration curves
are just the quantitiesy y ye Consequently, the last formula
becomess ;

v'(o) =Udglo ,

dx

i.e. the transverse intensity of turbulence at the end of the in=
jector tube may be obtained from the slope of the curve @ (x)
at that point. Figure 6 shows o as a function of x together with
the points determining the curves for the two cases under consid-
eration, L/M = 15 and L/M = 22. In the case L/M = 15 it appears.
that the curve wouid not extend back through the origin. It
seems likely that this is an effect of the dye injection method
used, The finite size of opening cf the injection tube will
have the effect of starting the dye wake with a positive value
of o right at the exit. However, this is in the wrong direction
to explain the behavior mentioned above. A discrepancy of this
type could also be caused by the following fact. The rate of
dye injection used was equivalent to an average velocity at the
exit of 2.2 ft/sec, that is, about 1.4 times the free-stream ..
velocity. The higher velocity of the jet will tend to postpone,
as a function of x, its diffusion. In particular, the substitu-
tion x = Ut used above will no longer be true, even approximately,
near the injector. Although correction for the finite size of
the injector would be relatively easy to carry out, correction
for the velocity discrepancy would be more troublesome and could
easily be avoided by more careful control of the injection rate.
In the present case, the slope was computed from the lower end
of the curve. Corrections would apparently have the effect of
changing the value of L/M somewhat but perhaps not very greatly
the actual slope at the sampling stations. In any case, it is
clear that more careful experimentation is needed. The two
slopes so obtained were used to compute the values of U/V!
shown in Figure 7. On the same figure are shown values vf
U/u' obtained with a hot-wire velocity meter in the same channel
with the same grid (M = 3/4") and with a smaller grid (M = 1/2").
The agreement seems better than the crudeness of the experiment
leads one to expect.

CRITIQUE OF METHOD

It seems clear from the analysis of the data obtained in
these experiments that the method will be more reliable as the
necessary corrections become smaller... This can only be accomplish-
ed by having the dimensions of the injector and sampler tubes
small in comparison with the scale of the turbulence. This will
generally be attained if the tube diameters are small compared
with the mesh width M. From dimensional considerations, increas-
ing the mesh width M while preserving the mesh Reynolds number
UM/y will not change the slope do/dx but will increase the dis-
tance from the end of the injector in which go is nearly a linear

o 7 =

aay Te ea
se RIE

function of x. Thus, by allowing measurements to be made farther
away from the injector, increasing M has the effect of making R,
the effective radius of the sampler smaller relative to the useful
values of @. In the present set of experiments = 0.03, M = 0.75
in.) the effective value of R/M = 0.040 seems to be still too

large to allow great confidence in the values of go after the very
substantial corrections were made. Since, however, the corrections
hecessary to obtain o, were less than 10 percent when 0 was as
large as 0.04, one can perhaps conclude that the scale of the
experiment should be so arranged that @)/R 91.5 over a sufficient
range in which o(x) is linear to computé a slope do(x)/dx fairly
accurately. If R is taken as 0.0175 in., corresponding to the
sampler actually used but with velocity matching the stream velocity
one must have 01>0.0%Hin. With a slope d@/dx = 0.04, correspond-
ing to L/M = 22, the first sampling station would then be at

x = 0.6 in. If one wishes to have at least another inch in the
linear range, a total of 1.6 in., the mesh of the grid should be
about double that in the present experiment, where the linear

range was about 3/4 in. long.

In the present experiments no effort was made to control
the rate of discharge of dye from the injector or the rate of
removal through the sampler except to try to keep them constant.
The rate of discharge should be adjusted to be equal to the free-
stream velocity and the rate of removal to be less than or equal
to it. The effect upon the flow of having a source and sink at
the injector and sampler, respectively, should again be small as
long as the diameters of the tubes are small compared with M.

The corrections applied to obtain the true values of ¢
from the experimental curves were based upon the assumption that
the true concentration curves were Gaussian curves. This has
not been tested. However, a test could be made by comparing the
experimental curves with theoretical curves obtained from a
Gaussian curve by local averaging as described in the appendix,
(i.e. by comparing the experimental g(r) curves with the theoretical
g(r) curves).

Gite

APPENDIX
DISCUSSION OF CORRECTIONS

It has been mentioned in the body of the report that the
finite size of the sampling tube will have an effect upon the
measured values of the dye concentration curves, This effect
may be estimated as follows if one assumes that the true dye
concentration curve is a generator of a circular Gaussian error
surface, Then the true curve will neve the equation

i
Rigue2

2no*

where r is the distance from the axis and A is some constant de=-
pending upon x, the distance from the injector to the sampler.
If one takes the radius of the opening of the sampler as R, the
curve actually obtained by measurement will be

2n Fe ee je? + pr+2 rp cos @
3 gt
r= aie i f a ef de
a) T R* > Seot < fers
which can be rewritten as Fi 4

i aed
gi= Ane? | £2? 1 (LB) ple

where Ip is the Bessel function of zero order with pure imaginary
argument. The procedure described for obtaining o was to com=
pute the indefinite piso et G(r) s ifn g(s)ds and determine o from
the condition G(@)/G(2) = 0.68, Although this would be correct
if the measured curve were f(r), it tends to overestimate win
the actual case. This correction could be computed from the ex-
pression for g(r) without a large amount of labor for a suffi-
cient range of values of r/@ and Réo . However, one may sub-
stitute for the circular opening of the sampler a square opening
of equal area without altering too greatly the correction and
with substantially less labor.

For the case of the Satake sampler of side 2R one replaces

g(r) by 3 ay | E pee a
Se vieep A Le a Go e di
LZ 2
A { / bee, | r+R i oa
g EE an ¢ "| 2R | ae Ir

i
u

The integrals occurring here have been well tabulated. For
convenience, let

xe

2h x p
2 S ord
pix) = = » PoO= if) pisids 5 Gr) =! Foods.

Then, after an interchange of order of integration, one obtains

Gi Af. mygif AB peck) - Reem) f(s) -p(egh]}

Cc
Also,
ete Alter: R
Glo) = fa ae P(E)
Consequently,

Gifts = 2{ HR pre) ARI p(le Rl) — 0) (8) p(reR]}

which holds for all values of r and R. Values for the functions
occurring here may be found in tables of the normal probability
function and the function G(r)/G(@) tabulated as a function of
r/o for various values of R/ao. Figure 8 shows a graph of these
functions for R/g = 0, 1, 2, 3, 42 A cross-plot may now be
gbtained from these curves for the particular value G(r/g, R/o)/
Gee,R/o) = 0.68. This gives a curve for Ré¢ against r/@ shown
in Figure “9, The correction to the value of g 4, say 0, obtained
from the experimental curve may now be made as follows: First
compute R' = R¥7W/2 in order to obtain the square opening of

area equal to that of the circular opening of radius R. Then
find the point (R'/go51) on the graph. The line passing through
the origin and this point will intersect the curve at some point
(R'/d15 Oo/01). The value of G, can then be found immediately,
and is the corrected value. This correction was made to all the
standard deviations taken from data. In one exceptional case,
for the data taken 3/4 in. downstream from the injector when this
in turn was 15 mesh lengths from the grid, the line through the
point(R'/gd 5, 1) and the origin did not intersect the curve at all.
This fact ae difficult to explain, for the indication is presum=-
-ably that the observed value of dg, is impossible. The dilemma
was resolved by ignoring the point.

It has been mentioned in the report that the total amount
of dye passing any one station should be a constant. However,
since the concentration curves obtained from the experiments
have been altered by the effect of the finite size of the -
sampler, one might expect that the volume under the rotated

=1 O=

measured curves would no longer be constant. It is possible

to compute this effect for the case of a circular Gaussian error
surface and a circular sampler. It has been shown above that
the altered distribution curve will be

g(r) = ee

a2
Then
[ go2mrde = 20a ZI ae adel I, (aa)dp
RAr
=A a ‘ Prrip(te? Prepae
— a 20r(”* -pY BY2
= Aaa ef, @ dp
=A.

Hence, the volume under the intensity surface is not changed by
the sampling procedure. It is of some interest to note that

this is not the case with a square sampler. A simple calculation
shows that

[Fl 2aedr = 7A PRA (2+ S)P4) a piesa

where p(x) and P(x) are the functions defined above. This function
has a very flat maximum of one at R/o = O, has scarcely deviated
from this value at R/o0 = 1 and ARORIGRO yw /4 as R/o —% co.

In order to find the value Up, it was necessary to plot
from the experimental data the Serres G(r)/G(ee), It would be
convenient if this work could be used to estimate the constant
A and to verify if possible its constancy as the value x, the
distance downstream from the injector, varies. Integrating

Sose(s)ds by parte, one gets

r 1
rGin-SGiads = [Lam-asids = otf (r- $2 J ds.

Consequently,

co a5
A= | amsgisids = 20 Gloo) { ie See als

os PES

This allows computation of A directly from the data. In the
process of finding the curve G(r)/G(o), it was necessary to find

the total area Ge) under the intensity curve g(v). The curves
appear somewhat as follows:

The integral J, (2-G(s)/G(o)] ds is then the shaded area. The
value of A may also be obtained directly from G(~) and the
corrected value of @in the following manners

e) oo pe a(R Ae
/ g(nidr =A fdr e a) soem re T,(454) Pd p

roy Ti Re g*

os Rh By, CW
Se eee ee eee

a
-R/o- - 372 pBY4

A I [x le

=4—1., de pe ie ee (6/4)

SO am EE lige) ie al
Dae | HRC oie

(2)
(R/2G)”
as A Rel -£ es fl
A epee ip (Ss T.(ndr
(R/20)”

-2 fis ;
If the indefinite integral (R/20) f, eT L(y is denoted
by S(R/v), one obtains the equation

ee 7 6S G(2)
Ae aye

In order to compute A it is necessary to have a table or graph
of the function S(R/ow). This is relatively easy to compute

from existing tables of the function @*%I,(x). A graph of

S(R/o) for values of R/o between O and 4 is shown in Figure 10.
On the same graph, for comparison, is shown the corresponding
function for a square sampler, S(R/7) = (a/R) f[e"“evrV2dp.
Since intensity data, in this report, are given nondimensionally
as fractions of the original dye solution, A will have the dimen-

sion of square inches.
o 12 3

se

ee

ye pi ‘OF
mayen
if

en

REFERENCES

Schubauer, G. B. = A Turbulence Indicator Utilizing the
Diffusion of Heat, NACA Report No. 524 (1935).

Taylor, G. I. - Diffusion by Continuous Movements, Proc.
London Math. Soc., 20, 196-212 (1921).

Taylor, G. I. = Statistical Theory of Turbulence, Proc. Roy.
Soc. London, 151A, 421-478 (1935).

Kalinske, A. A. and van Driest, BE. R. = Application of

Statistical Theory of Turbulence to Hydraulic Problems, Proc.

ese Cong. Appl. Mech., Cambridge, Mass., 416-421
1935).

Kalinske, A. A. and Robertson, J. M. = Turbulence in Open
Channel Flow, Engineering News-Record, 126, 539-541 (1941).

van Driest, E. R. - Experimental Investigation of Turbulence
Diffusion, Jour. Appl. Mech. 12, A91-A100, (1945).

-13-

u
Ain

Uy EW
eae

PA ore

cies 1

FLASK OF COMPRESSED AIR

GRID TO STIMULATE TURBULENCE

TTT EE ED BS TA 5 mae
apes i
Cam ae SAMPLER
oss
aM Py PROBE
eg
DIRECTION & a se ee eee
OF FLOW pa fi tae s 3
J ae Var
_ ee
Y

STEHT TITLED ET EET SD I RISES DP EH LH TG I SEM ESC TY RET TT
DYE INJECTOR

Sa = -
Figure 1 - Schematic Diagram of the Equipment Used in Dye |
Diffusion Measurements of Turbulence |

\ a, oe are

Figure 2 - Photograph Showing Test Section of the 1/22-Seale
Model of the TMB Circulating Water Channel and the

Arrangement of Apparatus

Micrometer

TMB 40511

Figure 3 - Sampler Used in Dye Diffusion Measurements
of Turbulence

ee ee ee
te ees)
| | YH peorsind Qo] |
pill by | Pho

I Te
Micrometer Aeaaing of Sacer Y, in inches

= sees
C)

i
|

Wen |
Eee
= Soeaoe

/JSGeeecee

, He
Seas aS
Bis SS Se sie)
ee
Pree se

L 189 193
Micrometer Reading of Sompler, Y,in inches

Figure 4— Cross-Stream Distributions of Dye Concentration IS Mesh-Lengths Behind a 3/4+Inch Mesh
at Various Positions,X, Downstream from Injector
Mean Stream Speed U=I.6 FtSec

Concentration of Dye, Per Cent of Original Pelee

AS
io way
ee ee ee

i
a
a
[teagonl YT
Same

os
a
Ele
Ea
ae
ae
Ee
Cle
a
ai
fe

Ogee
Oo oe

[4
ae

Poueeeee

Micrometer Reading of Sampler, Y, in Inches Micrometer Recaing. a Sampler, Y, in Inches

Figure 5— Cross-Stream Distributions of Dye Concentration 22 Mesh-Lengths Behind a 3/4—Inch Mesh
at Various Positions,X, Downstream from injector
Mean Stream Speed U=I.6 FtSec

0.07

006

Q.03

Q 02

0.01

0200
0.0 0.2 0.4 0.6 0.8 LAO) Wee 6a
x

Figure 6 = Corrected Standard Deviations for Dye Concentration
surveys

ok

ie
chris ae
1% pe i

ene:

\
Y

M = 3/4"
ODye Diffusion
Hot Wire

M = 1/2"
A Hot Wire

o 5 10 15 ae a 30 35 40
M
Figure 7 = Decay of Intensity of Turbulence in Water as Measured

by the Dye Diffusion and Hot-Wire Methods

LT ae
mw
Ae
oa, VK
rm Aare
LEAT
: LA
7 /anee
Waa

VA

Aisne 4

oad
begs

mt tie iff
IE

QI

GER) Gor) = 0.68

Figure 9 - Graphs of R& against rf for G (2) R)/G(e0 »R) = 0.68

s
i

iy
AAW oH

0.8

0.7

0.6

S(R/o’)
0.4

i (Reo)
S(R/o) = RjeoP i eT) da

0.3

Oel

Figure 10 - Graphs of S(R/o’) and 5(R/)

Reo
u me